The present invention relates to a constant false alarm rate (CFAR) processor for use in a radar receiver and, more particularly, to an adaptive CFAR processor which can maintain a constant false alarm rate against any probability density distribution function of clutter signal and offers a remarkable increase in target detectability.
Among known techniques for removing undesirable signals other than target signals in a radar system, a moving target indicator (MTI) has found extensive use which is designed to cancel returns from hills, buildings and like objects fixed in location. The MTI canceller, however, fails to effectively operate against those types of clutter having velocity components, e.g. sea clutter, weather clutter and angel echoes.
Various propositions have heretofore been made for suppressing clutters other than the returns from fixed objects. Typical of such propositions is the LOG/CFAR system (see J. Croney, "Clutter on Radar Display", Wireless Engineering, pp. 83-96, April 1956). The LOG/CFAR system has as its basis the assumption that the amplitude of a clutter signal (referred to simply as clutter hereinafter) has a probability density function which is a Rayleigh function. The system suppresses the clutter and reduces it to about the receiver noise level by sequential steps of logarithmically converting the clutter by a logarithmic converter which has a predetermined adequate characteristic constant, averaging the output of the logarithmic converter, subtracting the resulting average from a signal of interest, and subjecting the difference to an antilogarithmic conversion.
However, experiments have revealed that clutter residues still exist despite the LOG/CFAR processing. This originates from the fact that not all the clutters have probability density functions which conform to the Rayleigh function to which the LOG/CFAR technique is applicable. Rather, clutters generally have probability density functions which are expressed by the Weibull function except for limited cases. This was reported by D. C. Shleher in his paper entitled "Radar Detection in Weibull Clutter", IEEE Trans., AES-12, No. 6, pp. 736-743, 1976. Apart from the Weibull function, clutters having the Log-Normal function or Rice function cannot be coped with by the LOG/CFAR system.
For the CFAR processing of clutter having the Weibull function (referred to as Weibull clutter hereinafter), a technique using equations disclosed in U.S. Pat. No. 4,318,101 to convert the Weibull clutter into the Rayleigh clutter may be advantageously practiced since an ordinary LOG/CFAR circuit suffices for this purpose. The subject of this technique is a clutter X of the Weibull function which is expressed as EQU Pw(X)=(K/.sigma.)(X/.sigma.).sup.K-1 .multidot.exp {-(X/.sigma.).sup.K }(1)
Then, using a scale parameter .sigma. and a shape parameter K obtained from the clutter, a variable conversion of the clutter X is executed as EQU Z=.sigma.(X/.sigma.).sup.K/2 ( 2)
The resultant signal has a probability density function which is the Rayleigh function and given by EQU P.sub.R (X)=(2X/.sigma..sup.2).multidot.exp {-X.sup.2 /.sigma..sup.2 }(3)
(a function provided by substituting 2 for the K of equation (1)).
Such a technique is not fully acceptable because it is ineffective against clutters having other types of functions (such as a Log-Normal function and a Rice function), that is, it finds application only to Weibull clutter.
V. G. Hansen proposed a technique for suppressing clutters having any type of function (any type of probability density function) in his paper entitled "Constant False Alarm Rate Processing in Search Radars" presented in an International Conference on RADAR--PRESENT AND FUTURE held on Oct. 23-25, 1973. Whatever the cumulative distribution function q.sub.w (X) of clutter may be, the technique performs a variable transformation on the clutter as EQU Z=-log [1-q.sub.w (X)] (4)
so that the probability density function of the resultant signal is transformed into an exponential function e.sup.-z.
It is true that the Hansen's technique can convert clutter into a signal having a predetermined exponential function regardless of the type of the probability density function of the clutter. This technique still involves some problems, however. The abovementioned exponential function is a function derived from the Weibull function of equation (1) in which the K is replaced by 1 and, therefore, it is included in the Weibull function. Considering the relationship between the threshold value and the false alarm rate in CFAR processing Weibull clutter, it is known that the false alarm rate for a common threshold value decreases with the increase in the shape parameter K. It is also known that the variance Var(Z) obtainable with a LOG/CFAR circuit decreases with an increase in the shape parameter K. For details, see the paper "Suppression of Weibull-Distributed Clutters Using a Cell-Averaging LOG/CFAR Receiver" by M. Sekine et al., IEEE trans., AES-14, No. 5, pp. 823-826, September 1978, particularly FIG. 3 on p. 825, and the aforementioned paper "Radar Detection in Weibull Clutter" by D. C. Schleher, FIGS. 2-6, and a paper "Suppression of Radar Clutter" by Sekine et al., the Institute of Electronics And Communication Engineers of Japan, Trans. IECE, Vol. 62-B, No. 1, 1979, pp. 45-49, particularly FIGS. 3 and 4. Since the exponential function is the function given by substituting 1 for the shape parameter K in the Weibull function, the false alarm rate grows larger than in the case of a Rayleigh function wherein K=2. Moreover, a smaller shape parameter K needs a larger threshold value which would even cancel target signals of relatively low levels and depart from the function expected for a radar system.
As discussed above, of the prior art systems, one relying on the variable conversion of equation (2) cannot process clutters other than Weibull clutter for a constant false alarm rate. The Hansen system using the variable conversion of equation (4) can perform CFAR processing regardless of the type of the probability density function of clutter. Still, this holds true only in the theoretical aspect; in practice, due to the shape parameter which is fixed at a value of 1, not only is a small false alarm rate unavailable but a large threshold value is necessary for the CFAR processing. Such a threshold value would cancel target signals together with clutters, resulting in a poor target detectability.